arXiv subjects

Liang Jiang

Publications and source records attributed to Liang Jiang.

At least 19 recordsLinked to original sources

arXiv2026

High-Rank Encoding Can Improve Approximate Quantum Error Correction

Conventional quantum-code constructions encode pure logical states as pure code states, but this restriction can sacrifice performance. We show that intrinsic encoding randomness can improve optimal entanglement fidelity. We bound the loss from imposing a rank-one encoder and prove it is at most quadratic near perfect recovery after joint optimization. The optimized advantage survives small noise perturbations. An explicit noise family requires higher-rank encoders arbitrarily close to perfect recovery, with every optimal encoder mapping pure inputs to mixed code states.

quant-ph↗

arXiv2026

Robust Code RL via Faulty-Code-Driven Test case Synthesis and Dense Reward Shaping

Reinforcement Learning from Verifiable Rewards (RLVR) is pivotal for enhancing LLM code generation, yet its efficacy is often hindered by insufficient test case coverage, leading to reward hacking and policy degradation. To address this, we propose RobustTests, a framework featuring a faulty-code-driven test case synthesis strategy. By leveraging "near-correct" faulty codes, RobustTests captures latent logical discrepancies and employs validator agents with behavioral feature clustering to filter invalid or redundant test cases. Additionally, a stepwise dense reward function based on pass rates is introduced to mitigate false negatives and enhance training robustness. Using this pipeline, we construct an augmented version of the CodeContests+ dataset with superior diagnostic utility. Experimental results show that RL fine-tuning of Qwen3-32B via RobustTests achieves a 3% absolute gain on LiveCodeBench, demonstrating its effectiveness in advancing LLM code generation proficiency. Codes and data are available at https://huggingface.co/datasets/sid6/RobustTests.

cs.AI↗

arXiv2026

Integer Linear Programming Decoder for Abelian and Non-Abelian Topological Codes

Topological orders (TOs) are widely used as quantum error-correcting codes, with anyon excitations serving as error syndromes. For certain Abelian TOs, decoding can be performed by independently matching particle-antiparticle pairs of each species. However, matching-based decoders cannot handle more general fusion rules in either Abelian or non-Abelian TOs, nor account for noise that correlates different anyon species. While clustering decoders are more broadly applicable, they typically neglect anyon data and fusion properties, leading to poor performance in practice. In this work, we introduce a fundamentally different decoder for arbitrary TOs based on integer linear programming (ILP). The ILP formulation linearizes the error-correction problem through the introduction of auxiliary variables and encodes fusion rules as linear constraints. Classical optimization then identifies the minimum-weight error configuration. As concrete examples, we determine error-correction thresholds for three TOs: the Abelian $\mathbb{Z}_2$ TO under depolarizing noise, where charge and flux errors are correlated; the Abelian $\mathbb{Z}_3$ TO, which does not admit a pairwise matching decoder; and the non-Abelian $D_4$ TO under noise channels that generate all anyon species. We demonstrate the versatility of the ILP decoder by showing a clear performance advantage over most existing decoders in all three cases. We further extend the method to incorporate noisy syndrome measurements and propose a just-in-time variant for continuous error correction. Our results establish ILP as a natural framework for handling correlated errors and general anyon fusion rules, and as a powerful and flexible general-purpose decoder for incoherent anyon noise in arbitrary TOs, with applications to fault-tolerant quantum computation.

quant-ph↗

arXiv2026

Global Precision Bounds and Success-Probability Guarantees in Quantum Parameter Learning

Quantum metrology offers the possibility of quantum enhancements of the precision of various sensing tasks. In this manuscript, we tackle two open problems in the theory of single-shot quantum parameter learning, going beyond the usual setting of local parameter estimation via repeated measurements. The first concerns the construction of global upper bounds on the learning precision. The second concerns rigorous guarantees on the success probability of parameter learning, namely, lower bounds on the probability of learning a parameter with a certain precision, given the constraints on the resources used for the quantum metrology task. We provide rigorous, practical, and global upper bounds and success-probability guarantees for quantum parameter learning. Most importantly, we establish a fidelity-based learning guarantee for generic mixed-state models that can be viewed as the achievability-side analogue of the quantum Cramer-Rao bound. Whereas the latter provides a no-go constraint, based on the local curvature of the fidelities, our bound uses only pairwise fidelities between parameter-encoded states to certify that a prescribed precision is attainable with a guaranteed success probability. We demonstrate the versatility of the new bounds in a Rabi-frequency-learning example involving a driven qubit coupled to a bosonic environment and a collective-spin Hamiltonian learning problem. Together, the new global bounds and success-probability guarantees allow us to rule out unattainable precision and to certify attainable precision beyond what is possible via standard Fisher-information analysis or binary hypothesis testing bounds. They also allow one to tractably characterize the performance of various learning schemes, without the overhead of an explicit simulation.

quant-ph↗

arXiv2026

Active-SWE: Benchmarking Coding Agents for Proactive Bug Fixing without Issue Reports

Coding agents powered by large language models (LLMs) are increasingly adopted in software engineering (SWE) scenarios, capable of fixing a specific bug in large-scale codebase. However, existing SWE benchmarks typically assume that high-quality issue reports with detailed information are always available, which is easily violated in practice due to the complexity of report acquisition and curation. To address this, we introduce Active-SWE, a benchmark for evaluating coding agents on proactively discovering and fixing multiple bugs without report guidance, covering 1,663 tasks across six bug categories and eight languages. Beyond shifting the focus from existing reactive bug fixing to proactive bug fixing, Active-SWE enables a more in-depth evaluation by expanding the scope from fixing a specific recorded bug to multiple-bug fixing and potential bug discovery scenarios. To construct Active-SWE, we propose a novel difficulty-aware task formulation pipeline with a dual-track evaluation framework, facilitating comprehensive evaluation of proactive bug-fixing capability. Extensive experiments reveal that most state-of-the-art coding agents struggle with proactive bug-fixing tasks, demonstrating limited performance in locating and resolving recorded bugs, handling multiple bug fixing scenarios, and discovering valid potential bugs.

cs.SE↗

arXiv2026

Quantum channel learning with limited parallel access

Quantum channels can characterized by their action on an orthogonal operator basis, where these operators are related to observable properties of the quantum system. For qudit and multimode bosonic systems, this is encoded respectively in the Heisenberg--Weyl transfer matrix estimated from the Choi state, and in the characteristic-function transfer function estimated from the Choi state generated by probing with a two-mode squeezed vacuum state. We derive sample-complexity bounds for estimating entries of these transfer matrix/function to additive accuracy $\epsilon$ with success probability $\geq1-\delta$, under different resources: access to the complex-conjugate channel $\mathcal{E}^*$ and/or simultaneous access to $c$ copies of the channel. In all settings, the learner uses parallel channel calls with adaptively chosen, ancilla-assisted input states and measurements. Absolute values of transfer-matrix entries can be learned efficiently with simultaneous access to $\mathcal{E}$ and $\mathcal{E}^*$, with tight scaling $\epsilon^{-4}$. Without conjugate access, any $c<d$ copies are insufficient for efficient learning, requiring sample complexity exponential in the number of ($d$-level) qudits $n$ (for prime $d$). Efficiency is recovered at $c=d$, with tight scaling $\epsilon^{-2d}$. For bosonic systems, exponential sample complexity persists for all $c=O(1/\epsilon)$. Although the task is learning a particular state, these bounds carry stronger implications than standard state-learning bounds since the learner controls the inputs and ancillary assistance. This establishes a hierarchy of channel-learning resources: self-complex-conjugate channels require two-copy ancilla-assisted access for efficient learning, while for every square-free $d$, some channels require $d$-copy access. As a corollary, we bounds tighter lower bounds for state learning with limited multi-copy access.

quant-ph↗

arXiv2026

Logical computation with canonical lifted product codes

High-rate quantum low-density parity-check (qLDPC) codes encode many logical qubits with low physical-qubit overhead, but realizing efficient fault-tolerant computation on such dense encodings remains a major challenge. Generic, code-agnostic techniques such as code surgery and gate teleportation apply broadly, but are difficult to make modular, low-overhead, and fully certifiable on complex high-rate codes whose structure is left unexploited. Here we overcome these obstacles by co-designing the code together with its logical instruction set for a broad family of \emph{canonical} lifted-product (LP) codes with cyclic symmetry. We show that these codes admit a \emph{canonical logical basis}, in which conjugate logical operators are organized into rows and columns of cyclic orbits inherited directly from the underlying classical codes, analogous to the structure that makes hypergraph-product codes so tractable. This canonical basis unlocks a complete logical instruction set, including constant-depth automorphism and fold-transversal Clifford gates, modular graph code surgeries built from a constant number of reusable seed surgery gadgets or a compact canonical extractor, highly parallel logical Pauli-product measurements, and parallel magic-state injection. For example, a $[[1122,148,\leq\!20]]$ (resp. $[[4350,1224,\leq\!20]]$) LP code requires only two (resp. four) seed surgery gadgets, while arbitrary high-weight logical measurements can be implemented using a full extractor smaller than half of the data code block. These results advance the frontier of fault-tolerant quantum computation on ultra-high-rate quantum architectures.

quant-ph↗

arXiv2026

Strategic Plan for Neutral Atom Quantum Computation

We present a strategic plan for neutral atom quantum computation, bringing together hardware development and theory advancements to achieve the goal of practical quantum advantage. The concept of practical quantum advantage is defined, along with how to verify claims of advantage, and approaches to designing quantum algorithms that deliver practical advantage. Future directions for neutral atom quantum processor hardware are described: scaling-up system size, Qubit encodings and atomic platforms, going further below threshold with neutral-atom logical-qubit performance, continuous reloading of qubits, and fast readout. We also explore opportunities for scalable integrated photonic control technologies. Alongside hardware advancements, new developments in quantum error correction and compilation of quantum circuits are proposed. Finally, we examine the opportunity of networking multiple neutral atom quantum processors together to perform distributed quantum computing and overcome possible limitations of a single system.

quant-ph↗

arXiv2026

Enhancing Entanglement Purification with Shared Randomness

Entanglement purification protocols (EPPs) are essential for improving entanglement fidelity to support fault-tolerant distributed quantum information processing. Practical entanglement sources are often heterogeneous and source labels may be unavailable at the EPP layer. We show that classical shared randomness, together with buffer memories, can enhance entanglement purification when source labels are unavailable, without state characterization or EPP circuit optimization. The strategy is to accumulate multiple entanglement distribution rounds and then use shared randomness to shuffle all the stored entangled states before packaging them as inputs to the EPP. For any $n$ Werner sources and any fixed $n$-to-1 bilocal Clifford EPP, we prove that accumulating and shuffling improves the expected success probability and the success-weighted output Bell fidelity over the baseline without accumulating and shuffling, for every $n$, for every finite number of accumulation rounds and in the asymptotic limit, and the improvement increases monotonically with the number of accumulation rounds.

quant-ph↗

arXiv2026

Experimental Realization of Synthetic Magnonic Lattice via Floquet Engineering

Magnonic systems, which exploit spin-wave excitations in magnetic materials, offer a promising platform for coherent information processing due to their low dissipation, strong nonlinearities, and intrinsic nonreciprocity. However, scaling magnonic circuits remains challenging, particularly with low-loss insulators such as yttrium iron garnet (YIG), which are difficult to pattern. Here, we experimentally realize a synthetic dimension in a magnonic system by coupling multimode magnon resonances in the frequency domain using time-periodic Floquet modulation. This approach enables electronically tunable interactions between discrete modes within a single YIG device, forming a reconfigurable mode-space lattice that supports functionalities such as Bloch oscillation. Our results demonstrate that high-dimensional magnonic dynamics can be achieved without increasing device footprint, establishing synthetic dimensions as a scalable and programmable route for integrated magnonic technologies. This advancement positions magnonic systems as promising platforms for engineering emergent phenomena that are inaccessible at equilibrium.

cond-mat.mes-hall↗

arXiv2026

Ling and Ring 2.6 Technical Report: Efficient and Instant Agentic Intelligence at Trillion-Parameter Scale

Efficient and scalable agentic intelligence requires models that can deliver both low-latency responses and strong reasoning capabilities while remaining practical to train, serve, and deploy. In this report, we present Ling-2.6 and Ring-2.6, a family of models designed to address this challenge at scale. Ling-2.6 is optimized for instant response generation and high capability per output token, whereas Ring-2.6 is tailored for deeper reasoning and more advanced agentic workflows. Instead of training from scratch, we upgrade the Ling-2.0 base model through architectural migration pre-training and large-scale post-training. This upgrade is guided by a unified co-design of model architecture, optimization objectives, serving systems, and agent training environments, enabling improvements in both model capability and deployment efficiency. At the architectural level, we introduce a hybrid linear attention design that integrates Lightning Attention with MLA, improving the efficiency of long-context training and decoding. To further enhance token efficiency, we optimize capability per output token through Evolutionary Chain-of-Thought, Linguistic Unit Policy Optimization, bidirectional preference alignment, and shortest-correct-response distillation. For agentic capabilities, we propose KPop, a reinforcement learning framework designed to support stable training of Ring-2.6-1T on large-scale environment-grounded data. KPop improves training efficiency through asynchronous scheduling across coding, search, tool use, and workflow execution, enabling scalable learning from complex agent-environment interactions. Together, Ling-2.6 and Ring-2.6 provide a practical pathway toward efficient, scalable, and open agentic systems. We open-source all checkpoints in the 2.6 family to support further research and development in practical agentic intelligence.

cs.CL↗

arXiv2026

Learning Mid-circuit Measurement Backaction from Three Repeated Measurements

Accurate modeling of mid-circuit measurements (MCMs) is essential for dynamic-circuit operations such as syndrome extraction, measurement-based reset, and the separation of state-preparation and measurement (SPAM) error. Unlike terminal measurement, a noisy MCM both produces a classical outcome and alters the incoming quantum state, thereby influencing subsequent circuit operations. This makes conventional confusion-matrix or fidelity-level characterization insufficient. Here we introduce an efficient, self-consistent protocol for learning a single-qubit Z-twirled MCM instrument, retaining the readout-backaction correlations and excitation-decay asymmetry that are erased in Pauli-error descriptions. Remarkably, readout bit strings from only three repeated MCMs on a maximally mixed input determine all learnable parameters of the reduced instrument, up to a single unidentifiable gauge degree of freedom. Physicality constraints convert this non-identifiability into narrow, gauge-aware error intervals. Implemented on IBM superconducting processors, the learned instrument improves Pauli-observable prediction by ${\sim}100\times$ over a conventional confusion-matrix model and reveals a $T_1$-decay dominated backaction. Our protocol provides a compact characterization layer for SPAM error separation, reset optimization, and noise-aware quantum error correction.

quant-ph↗

arXiv2026

Realistic Simulation of Quantum Repeater with Encoding and Classical Error Correction

Quantum repeaters are essential for scalable long-distance quantum networking. As quantum information processing moves toward fault-tolerant and error-corrected operations, it becomes increasingly important to study quantum repeaters that also move beyond raw physical entanglement and towards logical entanglement. In this paper, we implement and simulate the quantum repeater with encoding and classical error correction (QRE-CEC) protocol in SeQUeNCe, a discrete-event simulator of quantum networks. The protocol distributes logical Bell pairs, performs encoded entanglement swapping, and uses classical error correction for the decoding of entanglement swapping measurement outcomes to determine Pauli-frame corrections. For this study, we extend SeQUeNCe with a stabilizer-based backend, add support for CSS code-based encoded operations, and integrate gate, measurement, idle decoherence, and state-initialization noise models. Our simulation results show that QRE-CEC suppresses all modeled errors to the second order. Also, QRE-CEC can distribute logical Bell pairs with 0.91 fidelity over a distance of 2000 km under the parameter regimes we study. Beyond protocol-level performance evaluation, our implementation exposes practical simulator and control-plane challenges that are typically abstracted away in theoretical studies.

quant-ph↗

arXiv2026

Quantum advantages for syndrome-aware noisy logical observable estimation

Recent progress in fault-tolerant quantum computing suggests that leveraging error-syndrome information at the logical layer can substantially improve performance, including the estimation of logical observables from noisy states. In this work, based on quantum estimation theory, we develop an information-theoretic framework to quantify the utility of error syndromes for noisy logical observable estimation. We distinguish two operational regimes of such syndrome-aware protocols: classical protocols, in which the logical measurement basis is fixed and syndrome information is used only in classical post-processing, and quantum protocols, in which the logical quantum control can be tailored to depend on the observed error syndrome. For classical syndrome-aware protocols, we prove a universal limitation: on average, syndrome information can improve the effective logical error rate by at most a factor of two, implying at most a quadratic reduction in sampling overhead. In contrast, once syndrome-conditioned quantum control is permitted, we demonstrate that the effective logical error rate decays exponentially with the number of code blocks. These findings provide fundamental guidance for designing future fault-tolerant architectures that actively exploit syndrome records rather than discarding them after decoding.

quant-ph↗

arXiv2026

Universal Sample Complexity Bounds in Quantum Learning Theory via Fisher Information Matrix

We show that the sample complexity required in quantum learning theory within a general parametric framework is fundamentally governed by the inverse Fisher information matrix. More specifically, we derive upper and lower bounds on the number of samples required to estimate the parameters of a quantum system within a prescribed small additive error, with high success probability under maximum-likelihood estimation. Notably, both the upper and lower bounds are determined by the supremum of the maximum diagonal entry of the inverse Fisher information matrix. We then apply the general bounds to Pauli channel learning and Pauli expectation value learning, which serve as representative tasks in quantum channel and state learning, respectively, in the asymptotic small-error regime. Furthermore, we identify the structural origin of exponential sample complexity in Pauli channel learning without entanglement and in Pauli expectation value learning without quantum memory by comparing the quantum Fisher information matrix and the classical Fisher information matrix. We then extend the analysis to an error criterion based on the Euclidean distance between the true parameter values and their estimators, deriving the corresponding upper and lower bounds on the sample complexity, which are likewise characterized by the inverse Fisher information matrix. As an application, we consider Pauli channel learning with entangled probes. We highlight two fundamental contributions to quantum learning theory. First, we establish a systematic framework that determines the task-independent sample complexity under maximum-likelihood estimation. Second, we show that, in the small-error regime, the learning sample complexity is governed by the inverse Fisher information matrix, which is the central quantity in quantum metrology that determines the ultimate achievable mean squared error.

quant-ph↗

arXiv2026

Passive Environment-Assisted Quantum Communication

As quantum information systems mature, efficient and coherent transfer of quantum information through noisy channels becomes increasingly important. We examine how passive environment-assisted quantum communication enhances direct quantum information transfer efficiency. A bosonic pure-loss channel, modeled as transmission through a beam splitter with a vacuum input state at the dark port, has zero quantum capacity when transmissivity is below 50%. Quantum communication through the channel can be enhanced by passive environment assistance, achieved via the selection of an appropriate input state for the ancilla port. Although ideal Gottesman-Kitaev-Preskill (GKP) states enable perfect quantum information transmission at arbitrarily small transmissivity, they are challenging to realize experimentally. We therefore explore more experimentally accessible non-Gaussian ancilla states, such as Fock, cat, and squeezed cat states, and numerically determine the optimal encoding and decoding strategies. We also construct analytical schemes that yield high-fidelity transmission and good information rates.

quant-ph↗

arXiv2026

Approaching the Limit in Multiparameter AC Magnetometry with Quantum Control

Simultaneously estimating multiple parameters at the ultimate limit is a central challenge in quantum metrology, often hindered by inherent incompatibilities in optimal estimation strategies. At its most extreme, this incompatibility culminates in a fundamental impossibility when the quantum Fisher information matrix (QFIM) becomes singular, rendering joint estimation unattainable. This is the case for a canonical problem: estimating the amplitude and frequency of an AC magnetic field, where the generators are parallel to each other. Here, we introduce a quantum control protocol that resolves this singularity. Our control protocol strategically engineers the sensor's time evolution so the generators for the two parameters become orthogonal. It not only removes the singularity but also restores the optimal scaling of precision with interrogation time for both parameters simultaneously. We experimentally validate this protocol using a nitrogen-vacancy center in diamond at room temperature, demonstrating the concurrent achievement of the optimal scaling for both parameters under realistic conditions.

quant-ph↗

arXiv2026

Quantum superresolution and noise spectroscopy with quantum computing

Quantum metrology of an incoherent signal is a canonical sensing problem related to superresolution and noise spectroscopy. We show that quantum computing can accelerate searches for a weak incoherent signal when the signal and noise are not precisely known. In particular, we consider weak Schur sampling, density matrix exponentiation, and quantum signal processing for testing the rank, purity, and spectral gap of the unknown quantum state to detect the incoherent signal. We show that these algorithms are faster than full-state tomography, which scales with the dimension of the Hilbert space. We apply our results to detecting exoplanets, stochastic gravitational waves, ultralight dark matter, geontropic quantum gravity, and Pauli noise.

quant-ph↗